Time Series: Advanced methods

Abstract

Recent developments in the time-domain analysis of time series are reviewed. The concept of dynamical systems serves as a unifying theme of the review. We consider first methods for the modelling of the drift component or the conditional mean of a time series. This includes the class of threshold models and its variants. We then consider methods for the modelling of the diffusion component or the conditional variance of a time series which includes the popular generalized autoregressive conditional heteroscedastic G(ARCH) models and the stochastic volatility (SV) models. Hybrid models for the modelling of both the drift and the diffusion are then introduced. Long memory and discrete-valued time series models are also included. The main focus is on univariate series although multivariate series are also mentioned where appropriate.